20 and 30 (mb) had special names; 40-90 were named as if plurals of the units 4-9, as in Semitic. 100, fat; 1000, ~,; 10,000, zb; 100,000, lifnw.

Expressing this condition we obtain mb = 1/ nc = o as the relation which must hold between the co-efficients of the above equation and the sides of the triangle of reference for the equation to represent a parabola.

If the co-ordinate axes coincide with the principal axes of this quadric, we shall have ~(myz) =0, ~(mzx) =0, Z(mxy) = 0~ (24) and if we write ~(mx) = Ma, ~(my1) = Mb, ~(mz) =Mc2, (25) where M=~(m), the quadratic moment becomes M(aiX2+bI,s2+ cv), or Mp, where p is the distance of the origin from that tangent plane of the ellipsoid ~-,+~1+~,=I, (26)

Provided ~(mx2) = Ma, ~(my) = Mb, ~(mzi) = Mc2

If all the masses lie in a plane (1=0) we have, in the notation of (25), c2 = o, and therefore A = Mb, B = Ma, C = M (a +b), so that the equation of the momental ellipsoid takes the form b2x2+a y2+(a2+b2) z1=s4.

Thus taking nny point 0 as base, we have first a linear momentum whose components referred to rectangular axes through 0 are ~(m~), Z(m~), ~(mb); - (I)

It may be shown that if the distance of the carried point from the centre of the rolling circle be mb, the equation to the epitrochoid is x = (a+b) cos 0 - mb cos (a+b/b)0, y = (a +b) sin 9 - mb sin (a +b/b)0.